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MONT 103N -- Analyzing Environmental Data\\
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Midterm Examination -- March 30, 2012
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Your Name:  $\underline{\qquad\qquad\qquad\qquad\qquad\qquad}$
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{\it Directions:}  Do all work on these sheets.  You may use the back if necessary, but please
alert me with a note if you do.  In a case where a later part of a question depends on a previous
part, I will give credit for the later part as long as you have a correct approach, even without
the correct value from the previous part.  There
are 100 points, distributed as indicated in the questions.
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I.  In the absence of any natural predators, the population
in month $n$, denoted $u(n)$, of a fast-reproducing species of 
fruit flies satisfies the logistic difference equation:
$$u(n) = 2.3 u(n-1) - \frac{1.3}{300}\cdot (u(n-1))^2$$
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A)  (10)  If $u(0) = 100$, what are $u(1)$ and $u(2)$?
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B)  (10)  Now suppose that birds living in the same habitat
kill and eat $50\%$ of the fruit fly population present in
each month.  How could the model be adjusted to take this into
account?
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C)  (5) What are the equilibrium fruit fly populations
for your adjusted model in part B?
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II.  All parts of this question refer to the following data set:
$$17, 18, 19, 26, 27, 29, 38, 41, 48$$
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A)  (10) Find the ``5-number summary'' and draw the corresponding box plot.
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B)  (5)  Is the Bowley measure of skewness positive or negative for this data set?
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C)  (5)  What is the standard deviation (SD) of this data set?
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III.  Suppose that a data set of $n = 100$ lobster tail length measurements has been collected.
The mean shell length in the sample is $\overline{x} = 15$cm  and the SD is $5$cm.
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A) (5)  Would the $z$-score of a measurement $x = 12$ be?
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B) (5)  What length measurement would correspond to a $z$-score of $1.7$?
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C) (5)  Find a $95\%$ confidence interval for the population mean tail length.
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D) (10)   Estimate the proportion of the population of lobsters with tail lengths
between $13$ and $21$cm.  Are you assuming something here?
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IV.  Essay.  (30)  In Chapter 2 of {\it The Botany of Desire}, Michael Pollan says ``the tulip is that
rare figure of Apollonian beauty in a horticultural pantheon presided over by Dionysus,''
and ``color breaks can perhaps best be understood as an explosive outbreak of the Dionysian
in the too-strict Apollonian world of the tulip -- and the Dutch bourgeoisie.''  Explain
these statements:  Who (or what)
are Apollo and Dionysus?  What do they represent?  How did the figure of Dionysus
appear in Chapter 1 as well?
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